downward closed - meaning and definition. What is downward closed
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What (who) is downward closed - definition

A SUBSET OF A PARTIAL ORDER THAT INCLUDES ALL SUCCESSORS OF ITS ELEMENTS
Lower set; Down set; Down-set; Down-set lattice; Down set lattice; Downset lattice; Downward closed; Initial segment; Principal down set; Principal lower set; Principal down-set; Up-set; Upward closed set; Final segment; Upward closure; Downward closure; Downward closed set; Upper set and lower set; Upper and lower sets

downward closed         
Closed city         
  • An aerial view of [[Baikonur]], [[Kazakhstan]]
  • Zheleznogorsk]], in [[Krasnoyarsk Krai]], Russia
  • Zvyozdny]], Russia
  • A signboard for the Frontier Closed Area in Hong Kong
  • Map indicating federal subjects containing closed cities used for nuclear research and development
  • Washington]], US
  • [[Sarov Monastery]] in [[Sarov]], Russia (1904)
  • A view of [[Severomorsk]], [[Murmansk Oblast]], Russia, which is home to the [[Northern Fleet]].
  • A view of [[Seversk]], Russia
  • A street in [[Snezhinsk]], Russia
  • Snezhnogorsk]], Russia
SETTLEMENT WHERE SPECIFIC AUTHORIZATION IS REQUIRED TO VISIT
ZATO; Closed cities; Closed town; Closed administrative-territorial formation; Atomgrad; Atomgrads; Atomograd; Закрытые административно-территориальные образования; Zakrytye administrativno-territorial'nye obrazovaniya; Closed administrative-territorial formations; ЗАТО; List of closed cities; Russian closed city; Closed secret city
A closed city or closed town, not to be confused with a gated community, is a settlement where travel or residency restrictions are applied so that specific authorization is required to visit or remain overnight. Such places may be sensitive military establishments or secret research installations that require much more space or internal freedom than is available in a conventional military base.
Closed set         
SET WHOSE COMPLEMENT IS AN OPEN SET
Closed subset; Closed (topology); Closed sets; Closed (mathematics)
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points.

Wikipedia

Upper set

In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set ( X , ) {\displaystyle (X,\leq )} is a subset S X {\displaystyle S\subseteq X} with the following property: if s is in S and if x in X is larger than s (that is, if s < x {\displaystyle s<x} ), then x is in S. In other words, this means that any x element of X that is {\displaystyle \,\geq \,} to some element of S is necessarily also an element of S. The term lower set (also called a downward closed set, down set, decreasing set, initial segment, or semi-ideal) is defined similarly as being a subset S of X with the property that any element x of X that is {\displaystyle \,\leq \,} to some element of S is necessarily also an element of S.